NUMERICAL DETERMINATION OF MATERIALS CHARACTERISTICS FOR THE NEEDS OF SIMULATION AND ANALYSIS OF STALK CUTTING PROCESSES

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1 Krzysztof KUKIEŁKA Radosław PATYK Leon KUKIEŁKA Łukasz BOHDAL Przemysław BARTOSIK Koszaln Unversty of Technology Mechancal Engneerng Faculty ul. Racławcka Koszaln Poland e-mal: NUMERICAL DETERMINATION OF MATERIALS CHARACTERISTICS FOR THE NEEDS OF SIMULATION AND ANALYSIS OF STALK CUTTING PROCESSES Summary The am of ths work s to develop a numercal applcaton to determne the materals characterstcs and to smulate the phenomena of cuttng process by a sngle stalks and a few stalks as well as to present the possbltes of ts applcaton for smulaton of the cuttng process under real condtons - occurrng n cuttng assembles of typcal agrcultural machnery. An example of use of ths applcaton to the modellng of cuttng process of stalks n the cuttng system of the harvester Bzon s presented. The next stage wll be to develop a methodology to enable better desgn of the knfe unts used n a varety of agrcultural and forestry machnery and ther optmzaton. Key words: plants stalks stems cuttng smulaton analyss NUMERYCZNE WYZNACZANIE CHARAKTERYSTYKI MATERIAŁOWEJ NA POTRZEBY SYMULACJI I ANALIZY PROCESU CI CIA MATERIAŁÓW D BŁOWYCH I ŁODYGOWYCH Streszczene Celem nnejszej pracy jest opracowane aplkacj numerycznej do wyznaczana mechancznych charakterystyk materałowych symulacj zjawsk podczas procesu c ca pojedynczego d bła oraz klku d beł oraz przedstawene mo lwo c jej zastosowana do symulacj procesu c ca w warunkach rzeczywstych wyst puj cych w zespołach tn cych typowych maszyn rolnczych. Podano przykład zastosowana tej aplkacj do modelowana procesu c ca d bła w no ycowy zespole tn cym kombajnu zbo owego Bzon. Dalszym etapem b dze opracowane metodyk umo lwaj cej lepsze projektowane zespołów tn cych stosowanych w ró nych maszynach rolnczych le nych oraz ch optymalzacja. Słowa kluczowe: ro lny d bła łodyg c ce symulacja analza 1. Introducton The common tendency of mult-crtera optmzaton of modern agrcultural machnery assembles necesstates a thorough knowledge of the physcal phenomena occurrng durng operatons such as plowng sol seasonng cuttng of stalk materal squeezng commnuton etc. From modern machnes usually requre that the resultng product was on the hghest qualty but the cost of ts producton as low as possble. The dffculty n solvng the task as the optmzaton two-crteron s that physcal phenomena are geometrcally physcally and sometmes heat and nonlnear boundary condtons n the areas of contact of workng wth the materal are unknown. One of the fundamental processes occurrng n many agrcultural machnery (combnes mowers cane harvestng machnes machnes for harvestng wllow etc.) s the process of cuttng stalk materals. The theoretcal analyss [6] dstngushes between the followng possbltes of cuttng stalks: transverse oblque oblque sloped dagonal slanted at an angle to the plane of the stem longtudnal longtudnal - oblque longtudnal - axal. It s known that the process of cuttng stalk materal n two stages (squeezng and cuttng) [1 2 6]. However the practcal measurement of physcal phenomena occurrng n the real process of cuttng stalks s dffcult (or mpossble) due to the mpossblty of measurng such as the dstrbuton of pressure and frcton between the blade of a knfe blade and lners lack of knowledge of the mechancal characterstcs of the materal beng cut stalks etc. Therefore t s mpossble to analytcal soluton of the basc problem of such term dsplacement and deformaton states at any tme durng the process of cuttng stalks. Consequently t s mpossble to determne the optmum geometry of the blade and the lners n varous machnes. For example n a combne harvester dfferent companes use dfferent geometres of blades and fnger lner. Currently the development of technques and methods of modellng and smulaton makes the desgn process of cereal cuttng technology may be sgnfcantly expanded and mproved. Contemporary usng dfferent modellng methods such as physcs physcal mathematcal computer and consequently statstcal and modellng usng artfcal ntellgence. Each of these methods has advantages of modellng how defects. In physcal modellng statstcal and usng the artfcal ntellgence s necessary to buld a materal object and carryng out experments but does not requre knowledge of the physcal phenomena occurrng n the process. Ths approach requres a sgnfcant effort (tme and money) to perform the model and conduct experments. An alternatve to these methods of modellng can be: physcal modellng mathematcal and computer [7] but t requres knowledge of the physcs of the process but sgnfcantly can reduce spendng on the development of an adequate model of the test object. The am of ths work s to develop a numercal applcaton to smulate the phenomena of a sngle stalks the cuttng process and a few stalks and present the possbltes of ts applcaton to the smulaton of the cuttng process under real condtons - occurrng n group cuttng typcal agrcultural machnery for example use of ths applcaton to the modellng of cuttng stalks by the cuttng scssor n the harvester 72

2 Bzon. The next stage s to develop a methodology whch enable better desgn knfe assembles used for a varous of agrcultural and forestry tractors and as a result ther optmzaton. Due to the strong nonlnearty of the cuttng process usng fnte element method uses an updated Lagrangan formulaton and explct and mplct ntegraton algorthms derved the equatons of moton. It nvolves replacng the contnuous dscrete object model wth separate subvolumes and/or sub-areas restng on nodes [3 5]. In ths paper a model of the physcal process of consttutng the set phenomena assumptons and smplfcatons mathematcal model whch ncludes dfferental and algebrac equatons and nequaltes and functons condtonal on the bass of whch one can predct the course of physcal phenomena n the modelled process. Valdaton of the accuracy of developed mathematcal models and numercal algorthms and applcatons n the system ANSYS was made by comparng the smulaton results of a sngle stalks the cuttng process wth the results of expermental measurements. a) b) c) Fg. 2. Samples after cuttng for cuttng angle 0 : a) 100 mm mn -1 b) 300 mm mn -1 c) 500 mm mn -1 Rys. 2. Próbk po przec cu dla k ta c ca 0 : a) 100 mm mn -1 b) 300 mm mn -1 c) 500 mm mn -1 Measurement of a cross-samplng was done on the machne Werth (fg. 3). The dea developed a methodology to determne materal parameters based on the use of modellng and numercal smulaton and optmzaton procedures. 2. Determnaton of the characterstcs of the stalks materal Transverse cuttng stalks process were tested the stand for nvestgaton s shown n fgure 1 whch allows to obtan stalks for the test the force-dsplacement of the blade. Cuttng stalks made usng a flat blade wth a wdth of 1 mm. It allows the regstraton of the varaton of the force F as a functon of dsplacement l (fg. 1b) whch n turn permts the desgn of stalks the mechancal characterstcs of σ f ( ε) wth the selected propertes of a materal (type humdty etc.) once the technologcal parameters of the process (the speed of cuttng frcton condtons etc.). a) b) Fg. 1. Scheme of the tests (a) and testng machne Mecmesn (b) Rys. 1. Schemat wykonywana bada (a) maszyna wytrzymało cowa Mecmesn (b) When cuttng stalks confrmed lterature data [1 2] the exstence of two phases that s squeezng and cuttng approprate. In order to develop the characterstcs of σ f ( ε) or the test materal s requred beyond the knowledge of the characterstcs of F f ( Δl) measure cross-cut felds. Vew of the samples after cuttng for selected transverse cuttng speeds are shown n fgure 2. Fg. 3. Measurement of cross-sectonal area on the optcal measurng machne Werth Rys. 3. Pomar powerzchn przekroju poprzecznego na optycznej maszyne pomarowej Werth The numercal smulaton assumed that the stalks materal s homogeneous and sotropc and ts destructon after crossng the lmt of the normal or tangental stress. The real geometry of the stalks was replaced by a thn-walled ppe of crcular cross-secton wth a dameter d wthout elbows. The wall thckness was equal to the average thckness of the test stalk [8 9]. Based on the above assumptons the model s adopted to smplfy the elastc-plastc materal wth materal falure crteron for the maxmum values of normal ( Nmax ) and tangental ( Smax ) stresses. In the developed numercal model mapped the process of cuttng rye stalks consstent wth expermental experence. As desgn varables n the optmzaton process adopted values of materal parameters and approprate lmtatons were took [4]: σ σ E x v x N max S max 1 2 x x [ GPa] [ ] [ MPa] [ MPa]. The dea of the optmzaton process s the adjustment of materal parameters (desgn varables) wth the numercal model fathfully reproduces the behavour of the bologcal materal durng the cuttng process. As the optmzaton crteron was the value of the maxmum compressve force occurrng durng the smulaton process F Smax cuttng (1) 73

3 stalks. Whle the objectve functon s defned as the absolute value of the dfference of the maxmum force experenced durng the cuttng process by emprcal studes F Dmax and smulaton: F F F mn. (2) destnaton Smax D max Numercal analyzes were performed usng ANSYS. Stalk rye has been modellng as an object 3D n whch there s 3D state of stress and 3D state of stran. Stalk has been cut a sngle blade (fg. 4a). Fgure 4d shows the characterstcs of the resultant force to the dsplacement of the test stalks rye. It s consstent wth the results avalable n the lterature (fg. 4c) [1 2]. Was followed by the optmzaton process whch resulted n optmal (due to the crteron) values desgn varables. In the case of the selecton of materal parameters for the stalks rye amounted to respectvely the Young's modulus E 587 MPa Posson's rato ν 0072 materal falure crteron for the maxmum value of normal stress σ MPa and tangent σ 5924 MPa. S max N max In fgure 4d shows the characterstcs of the force to move the blade to the numercal model wth the optmal values desgn varables. Developed materal data (fg. 4b) have been mplemented to smulate the cuttng process n real condtons. Fg. 4. Vew of the dscreet numercal model (a) a graph σ f ( ε) of the cuttng stalks process along wth the phases [2] (c) cuttng force change as a functon of movement of the blade determned numercally and expermentally (d) Rys. 4. Wdok dyskretnego modelu numerycznego (a) opracowany wykres σ f ε przebeg procesu c ca d bła wraz z jego fazam [2] (c) zmana sł c ca w funkcj przemeszczena no a wyznaczona numeryczne eksperymentalne (d) 74

4 3. Applcaton of the cuttng process under real condtons Sample calculatons were performed for knfe assembly of the harvester Bzon for the sold model was developed based on the geometry shown n fgure 5. In computer smulatons assumed that the knfe and bayonet the fnger lner s made of a deally rgd materal and the blade has a materal elasto/vsco-plastc wth hardenng the Cowper-Symonds model: m Y [1+ ( /C)] ( Y0 + E p ) (3) where s the plastc stran hardenng parameter Y0 s the ntal statc yeld pont s the plastc stran rate ntensty C s the materal parameter defnng the effect of the plastc stran rate ntensty m 1/n s a materal constant defnng ts senstvty to the plastc stran rate s the plastc stran ntensty and Ep ET E/(E ET) s the materal parameter dependng on the modulus of plastc stran hardenng ET Y/ and Young s modulus E. A dscrete crackng approach was selected to model ductle frac- ture and element deleton method was adopted to smulate crack propagaton. A stran based materal separaton crteron avalable wth ANSYS for ths materal model was used n the smulatons. Accordng to ths crteron materal separaton occurs when the stran value of the leadng node s greater than or equal to a lmtng value. The lmtng stran was taken as ε 0 f 80 based on expermental nvestgatons. When an element of matrx materal reached the lmtng stran value the correspondng element would be deleted. The values of the constants for the stalk are taken as follows n ths study: C 40 s 1 and n 5 whle ρ 800 kg m -3 σ Y 0 8 MPa E 587 MPa ν E 6 T MPa and β 1. Dsregard effects of thermal phenomena. Dscretze geometrc model for the tetragonal fnte elements and nodes. On the bass of analytcal calculatons cuttng assembly combne set boundary and ntal condtons on the object of study t s bayonet wth fnger lner were fxed takng away translatonal and rotatonal degrees of freedom and the knfe was assumed lnear velocty V 25 m s -1. At ths stage speed resultng from the omsson of the operatng speed of the combne. Calculated states equvalent stresses and dsplacements of the axs states UZ shown n fgure 6. a) b) Fg. 5. Parts of the cuttng assembly of harvester Bzon: a) knfe b) bayonet wth fnger lner [10 11] Rys. 5. Cz c zespołu tn cego kombajnu Bzon: a) nó b) bagnet ze stalk [10 11] Fg. 6. The computer model of cuttng assembly (knfe and fnger lner) n harvester Bzon: a) dscretzaton b) boundaryntal condtons c) the state of dsplacement by axs UZ d) the equvalent stresses Rys. 6. Model komputerowy zespołu tn cego (nó stalka) kombajnu zbo owego Bzon: a) dyskretyzacja b) warunk brzegowo-pocz tkowe c) stan przemeszcze po os UZ d) stan napr e zredukowanych 75

5 Numercal applcaton allows the examnaton of the dsplacements strans stresses pressures n the contact zone and the forces nvolved n the process. The developed applcaton can take nto account the moton of the machne therefore take nto account the real condtons of the process. Ths approach enables the explanaton of physcal phenomena for dfferent cases of cut. In further studes t wll be possble to optmze the process for the dfferent boundary condtons for dfferent agrcultural and forestry machnery. 4. Conclusons 1. It was shown that t s possble numercal calculaton of the mechancal characterstcs of the stalk materal. Methodology based on mult-crtera optmzaton showed that the process of cuttng stalks desgnated numercally concdes wth the course set expermentally and are consstent wth the lterature. 2. Applcaton developed to smulate the process of cuttng stalks on the machne Mecmesn allows to determne the mechancal characterstcs of dfferent materals for dfferent ways to stalk cuttng. 3. Developed applcaton of ANSYS system allows for analyss of tme physcal phenomena occurrng n the process of cuttng stalks. It s possble: to present the modelled propertes of materals as a complex as a functon of stran and stran rate modellng the nteractons contact between the knfe and cut materal to examne by changng the nput data and model boundary condtons the qualtatve and quanttatve mpact of these nteractons on the cut process. The smulaton results can be used to desgn cuttng tools optmzed cereals. 5. References [1] Bochat A.: Teora konstrukcja zespołów tn cych maszyn rolnczych Wydawnctwa Uczelnane Unwersytetu Technologczno-Przyrodnczego w Bydgoszczy ISBN [2] Bochat A. Zastempowsk M.: Modelng the Dynamcs of the Vegetable Materal Detachment Process from Undsturbed Areas to Improve the Desgn of Selected Agrcultural Machnes. Transactons of the ASABE 56(4): (do: [3] Dacko M. Borkowsk W. Dobroc sk S. Nezgoda T. Weczorek M.: Metoda Elementów Sko czonych w mechance konstrukcj. Arkady Warszawa [4] Kukełka L.: Podstawy bada n ynerskch. PWN Warszawa ISBN [5] Kleber M.: Wprowadzene do metody elementów sko czonych. PWN Warszawa-Pozna ISBN [6] Kanafojsk C.: Teora konstrukcja maszyn rolnczych. Tom 2 cz I Maszyny do zboru ro ln d błowych łodygowych. PWN Warszawa ISBN ISBN X. [7] Pawłowsk T. Szczepanak J Współczesna metodyka projektowana weryfkacj konstrukcj maszyn rolnczych. In ynera Rolncza Nr 14 (74). s [8] Malnowsk E.: Anatoma ro ln. PWN Warszawa ISBN [9] wetlkowska K.: Surowce spo ywcze pochodzena ro lnnego. SGGW Warszawa ISBN [10] html [11] 76